The Computational Solution of Generalized Inverse Eigenvalue Problem for Pseudo-Jacobi Matrix - Fuxia Yi; Enhua Li (Journal of Mathematics)
This paper is concerned with two generalized inverse eigenvalue problems for a kind of pseudo-Jacobi matrix. From a non-Hermite matrix, an r×r Jacobi matrix, two distinct real eigenvalues, and part of the corresponding eigenvectors, an n×n pseudo-Jacobi matrix is constructed. Furthermore, an n×n pseudo-Jacobi matrix can be made by two different eigenpairs and a positive definite diagonal matrix. It is shown that a unique pseudo-Jacobi matrix can be recovered from partial eigenpairs and certain special mixed eigendata. Two algorithms are provided for the reconstruction of such a pseudo-Jacobi matrix, and illustrative numerical examples are presented to verify the proposed algorithms.